A new interface method for hyperbolic problems with discontinuous coefficients: One-dimensional acoustic example

A new numerical method, called the explicit simplified interface method (ES IM), is developed in the context of acoustic wave propagation in heterogene ous media. Equations of acoustics are written as a first-order linear hyper bolic system. Apart from interfaces, a standard scheme (Lax-Wendroff, TVD. and WENO) is used in a classical way. Near interfaces, the same scheme is u sed, but it is applied on a set of modified values deduced from numerical v alues and jump conditions at interfaces. It amounts to modifying the scheme so that its order of accuracy is maintained at irregular points. despite t he nonsmoothness of the solution. This easy-to-implement interface method r equires only a few additional computational resources, and it can be applie d to other partial differential equations. (C) 2001 Academic Press.